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@@ -5,14 +5,88 @@
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% Part: conclusions
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% Description:
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% summary of the content in this chapter
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-% Version: 01.01.2012
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+% Version: 01.09.2024
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\chapter{Conclusions 5}
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\label{chap:conclusions}
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+The states with the highest transmission rate
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+values are Thuringia, Saxony Anhalt and Mecklenburg West-Pomerania. It is also,
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+visible that all six of the eastern states have a higher transmission rate than
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+Germany. These results may be explainable with the ratio of vaccinated individuals\footnote{\url{https://impfdashboard.de/}}.
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+The eastern state have a comparably low complete vaccination ratio, accept for
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+Berlin. While Berlin has a moderate vaccination ratio, it is also a hub of
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+mobility, which means that contact between individuals happens much more often.
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+This is also a reason for Hamburg being a state with an above national standard
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+rate of transmission. Bremen has the highest ratio of vaccinated individuals,
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+this might be a reason for the it having the lowest transmission of all states.\\
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+
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+% -------------------------------------------------------------------
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+
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\section{Further Work}
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\label{sec:furtherWork}
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+Our findings demonstrate that with our methods enable the quantification of the
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+course of the COVID-19 pandemic in Germany using the data provided by the
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+Robert Koch Institute. Additionally, we present the limitations of our work.
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+The SIR model is subject to numerous limitations. For instance, it does not
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+account for individuals, who may be immune due to the vaccination status or
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+those who are not infectious due to quarantine. In this section, we explore
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+epidemiological models that illustrate these dynamics observed in real-world
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+pandemics and recommend further investigation for Germany. First, we examine
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+extensions of the SIR models, then we focus on agent-based models (ABMs).
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% -------------------------------------------------------------------
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-% insert further sections if necessary
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+\subsection{Further Compartmental Models}
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+As our results demonstrate, the SIR model is capable of approximating the
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+dynamics of real-world pandemics. However, the model is not without
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+limitations. As previously stated, the SIR model assumes that recovered
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+individuals remain immune and does not account for the reduction of exposure of
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+susceptible individuals through the introduction of non-pharmaceutical
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+mitigation policies, such as social distancing policies. These shortcomings can
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+be addressed by incorporating additional compartments and transmission rates
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+into the model. For example, the SEIRD model incorporates an \emph{Exposed}
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+group and subdivides the \emph{Removed} group into \emph{Dead} and
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+\emph{Recovered} compartments. Furthermore, this adds four additional rates to
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+the model: the contact rate, representing the average number of contacts
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+between infectious and susceptible people with a high probability of infection;
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+the manifestation index, indicating the proportion of individuals exposed to
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+the disease who will become infectious; the incubation rate, measuring the time
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+required for exposed individuals to become infectious; and the infection
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+fatality rate, quantifying the fraction of individuals who succumb to the
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+disease. As Doerre and Doblhammer~\cite{Doerre2022} show for Germany using a
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+numerical approximation method, for an SIERD model that they specialize to be
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+age- and gender-specific, that it shows the impact of non-pharmaceutical
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+mitigation policies. In their work, Cooke and van den Driessche~\cite{Cooke1996}
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+propose the SEIRS model with two delays. This is model is capable of
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+approximating diseases, that have an immune period, after which the recovered
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+individual becomes susceptible again. These are just a few examples of
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+the numerous modifications of the basic SIR model that can be used to
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+approximate and consequently quantify an pandemic.
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+
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+% -------------------------------------------------------------------
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+
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+\subsection{Agent based models}
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+
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+While compartmental models, such as the SIR model, look at the population as a
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+divided group, with each group representing a specific characterization that
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+all inhabitants of that group share, an \emph{Agent-Based Model} (ABM) sets its
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+focus on the individual. Each individual, or agent, has specific attributes
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+that determine its behavior and interactions with other agents during the
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+simulation. As Gilbert~\cite{Gilbert2010} states, ABMs simulate the behavior of
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+large groups, with each individual following simple rules. Kerr
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+\etal~\cite{Kerr2021} put forth a simulation tool, \emph{Covasim}, which they
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+base on an ABM. The ABM employs local data, including demographic data, disease
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+incidence data from the region, and contact data for household, schools and
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+workplaces, to define its simulation for a specific region. In their work,
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+Maziarz and Zach~\cite{Maziarz2020} address the criticism levied against ABMs
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+for simplifying the dynamics and lacking the empirical support for the
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+assumptions it they make. The authors utilize an ABM and the data specific to
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+Australia to demonstrate the efficacy of ABMs in portraying the dynamics of the
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+COVID-19 pandemic. They further state that ABMs can serve as serve as a tool
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+for assessing the impact of non-pharmaceutical mitigation policies. This
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+illustrates that ABMs play a distinct role in analyzing the COVID-19 pandemic.
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+As the data situation has evolved, it is imperative to investigate the
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+potential of utilizing ABMs as a tool to assess the pandemic's course.
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+
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+% -------------------------------------------------------------------
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